A convex lens and a concave lens, each having same focal length of `25 cm`, are put in contact to form a combination of lenses. The power in diopters of the combination is

Options

A. `25`
B. `50`
C. infinite
D. zero

Answer

To solve the problem, we need to find the power of a combination of a convex lens and a concave lens that are in contact with each other. Both lenses have the same focal length of 25 cm.

### Step-by-Step Solution:

1. **Identify the Focal Lengths**:
- The focal length of the convex lens (f1) is positive:
\[ f_1 = +25 \text{ cm} \]
- The focal length of the concave lens (f2) is negative:
\[ f_2 = -25 \text{ cm} \]

2. **Use the Formula for Equivalent Focal Length**:
- The formula for the equivalent focal length (F_eq) of two lenses in contact is given by:
\[ \frac{1}{F_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} \]

3. **Substitute the Values**:
- Substitute the values of f1 and f2 into the formula:
\[ \frac{1}{F_{eq}} = \frac{1}{25} + \frac{1}{-25} \]

4. **Calculate the Right Side**:
- Simplifying the right side:
\[ \frac{1}{F_{eq}} = \frac{1}{25} - \frac{1}{25} = 0 \]

5. **Determine the Equivalent Focal Length**:
- Since \(\frac{1}{F_{eq}} = 0\), this implies:
\[ F_{eq} = \infty \]

6. **Calculate the Power of the Combination**:
- The power (P) of a lens is given by the formula:
\[ P = \frac{1}{F_{eq}} \text{ (in meters)} \]
- Since \(F_{eq} = \infty\):
\[ P = \frac{1}{\infty} = 0 \text{ diopters} \]

### Final Answer:
The power of the combination of the convex lens and the concave lens is \(0\) diopters.

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